Simulating effects of temperature on acoustic microwave filters

ABSTRACT

A method of designing an acoustic microwave filter comprises generating a proposed filter circuit design having an acoustic resonant element with a defined admittance value, introducing a lumped capacitive element in parallel and a lumped inductive element in series with the resonant element, selecting a first capacitance value for the capacitive element and a first inductance value for the inductive element, thereby creating a first temperature modeled filter circuit design, simulating the first temperature modeled filter circuit design at a first operating temperature, thereby generating a first frequency response, selecting a second capacitance value for the capacitive element and a second inductance value for the inductive element, thereby creating a second temperature modeled filter circuit design, simulating the second temperature modeled filter circuit design at a second operating temperature, thereby generating a second frequency response, and comparing the first and second frequency responses to the frequency response requirements.

RELATED APPLICATION DATA

The present application is continuation of U.S. patent application Ser.No. 15/197,510, filed Jun. 29, 2016, which is a continuation of U.S.patent application Ser. No. 14/941,462, filed Nov. 13, 2015 (now U.S.Pat. No. 9,405,875). The foregoing applications are hereby expresslyincorporated by reference into the present application in theirentireties.

FIELD OF THE INVENTION

The present inventions generally relate to microwave filters, and moreparticularly, to acoustic microwave filters designed for narrow-bandapplications.

BACKGROUND OF THE INVENTION

Electrical filters have long been used in the processing of electricalsignals. In particular, such electrical filters are used to selectdesired electrical signal frequencies from an input signal by passingthe desired signal frequencies, while blocking or attenuating otherundesirable electrical signal frequencies. Filters may be classified insome general categories that include low-pass filters, high-passfilters, band-pass filters, and band-stop filters, indicative of thetype of frequencies that are selectively passed by the filter. Further,filters can be classified by type, such as Butterworth, Chebyshev,Inverse Chebyshev, and Elliptic, indicative of the type of bandshapefrequency response (frequency cutoff characteristics) the filterprovides relative to the ideal frequency response.

The type of filter used often depends upon the intended use. Incommunications applications, band pass and band stop filters areconventionally used in cellular base stations, cell phone handsets, andother telecommunications equipment to filter out or block RF signals inall but one or more predefined bands. Of most particular importance isthe frequency range from approximately 500-3,500 MHz. In the UnitedStates, there are a number of standard bands used for cellularcommunications. These include Band 2 (˜1800-1900 MHz), Band 4(˜1700-2100 MHz), Band 5 (˜800-900 MHz), Band 13 (˜700-800 MHz), andBand 17 (˜700-800 MHz); with other bands emerging.

Microwave filters are generally built using two circuit building blocks:a plurality of resonators, which store energy very efficiently at aresonant frequency (which may be a fundamental resonant frequency f₀ orany one of a variety of higher order resonant frequencies f₁-f_(n)); andcouplings, which couple electromagnetic energy between the resonators toform multiple reflection zeros providing a broader spectral response.For example, a four-resonator filter may include four reflection zeros.The strength of a given coupling is determined by its reactance (i.e.,inductance and/or capacitance). The relative strengths of the couplingsdetermine the filter shape, and the topology of the couplings determineswhether the filter performs a band-pass or a band-stop function. Theresonant frequency f₀ is largely determined by the inductance andcapacitance of the respective resonator. For conventional filterdesigns, the frequency at which the filter is active is determined bythe resonant frequencies of the resonators that make up the filter. Eachresonator must have very low internal resistance to enable the responseof the filter to be sharp and highly selective for the reasons discussedabove. This requirement for low resistance tends to drive the size andcost of the resonators for a given technology.

The duplexer, a specialized kind of filter is a key component in thefront-end of mobile devices. Modern mobile communications devicestransmit and receive at the same time (using LTE, WCDMA or CDMA) and usethe same antenna. The duplexer separates the transmit signal, which canbe up to 0.5 Watt power, from the receive signal, which can be as low asa pico-Watt. The transmit and receive signals are modulated on carriersat different frequencies allowing the duplexer to select them. Theduplexer must provide the frequency selection, isolation and lowinsertion loss in a very small size often only about two millimeterssquare.

The front-end receive filter preferably takes the form of a sharplydefined band-pass filter to eliminate various adverse effects resultingfrom strong interfering signals at frequencies near the desired receivedsignal frequency. Because of the location of the front-end receiverfilter at the antenna input, the insertion loss must be very low so asto not degrade the noise figure. In most filter technologies, achievinga low insertion loss requires a corresponding compromise in filtersteepness or selectivity.

In practice, most filters for cell phone handsets are constructed usingacoustic resonator technology, such as surface acoustic wave (SAW), bulkacoustic wave (BAW), and film bulk acoustic resonator (FBAR)technologies. The acoustic resonator has two resonances closely spacedin frequency call the “resonance” frequency and the “anti-resonance”frequency (see K. S. Van Dyke, Piezo-Electric Resonator and itsEquivalent Network Proc. IRE, Vol. 16, 1928, pp. 742-764). Such acousticresonators have the advantages of low insertion loss (on the order of 1dB at the center frequency), compact size, and low cost compared toequivalent inductor/capacitor resonators. For this reason, acousticresonator implementations are often used for microwave filteringapplications in the front-end receive filter of mobile devices. Acousticresonators are typically arranged in a ladder topology (alternatingseries and shunt resonators) in order to create band pass filters.Acoustic ladder filters have been very successful for handsetapplications, with more than a billion units currently sold each year.

The design of modern microwave filters with acoustic resonators requiresdetailed models to predict the frequency response of the filter. Thecustomary approach is to build an elaborate phenomenological model usingall geometrical aspects of each resonator, e.g., pitch, aperture,length, etc. Because commercial acoustic microwave filters must be ableto comply with performance requirements over a broad range oftemperatures, it is important to be able to model the performance of anacoustic microwave filter design over a relevant temperature range, sothat the filter design can be optimized to ensure that, when fabricated,it complies with the performance requirements over that temperaturerange. Thus, without an accurate model of the acoustic filter for theeffects of temperature, the acoustic filter cannot be designed oroptimized consistently.

The simplest and most common approach to accurately model an acousticfilter over a temperature range is to uniformly shift the filterresponse across the entire frequency range by an amount proportional tothe temperature. However, measurements of acoustic microwave filtersshow that this approach neglects the critical fact that the resonant andanti-resonant frequencies shift by different amounts for a giventemperature change. When constructed as part of a filter, this not onlyleads to the center frequency of the passband changing, but also thewidth of the passband changing. In particular, the change in theresonant frequencies of all the resonators moves the lower-frequencyedge of the filter, while the change in the anti-resonant frequencies ofall the resonators moves the higher-frequency edge of the filter, but atdisproportionate amounts to the resonant frequencies.

For example, referring to FIG. 1, the frequency response of an acousticmicrowave filter was measured at −20° C. (dotted line), 25° C. (solidline), and 100° C. (dashed line). As shown, the passband tends to shiftto lower frequencies as the temperature increases. Referring now to FIG.2, the frequency responses of an actual acoustic microwave filtermeasured at −20° C. and 100° C. (solid lines) can be compared tosimulated frequency responses of a corresponding acoustic microwavefilter design that have been proportionally shifted in accordance withthe two temperatures (dashed lines). It can be readily seen that, whenthe left sides of the passbands of the simulated frequency responses at−20° C. and 100° C. are respectively aligned with the left sides of thepassbands of the actual frequency responses at −20° C. and 100° C., theright sides of the passbands are not aligned, evidencing the fact thatthe passband not only shifts as the temperature changes, the passbandalso distorts as the temperature changes. Therefore, this simpleapproach incorrectly predicts a bandwidth unchanged by temperature.

A more sophisticated approach to modeling the effects of temperature isto characterize the individual resonators that make up a filter over arange of temperatures. Each model uses a certain number of parameters,which will vary with temperature. Using basic physical knowledge, onecan predict how each of these parameters will change as the temperaturechanges. The response of the resonator is captured with a sort ofanalytical model, e.g., Butterworth-van Dyke or Coupling-of-Modes (seeA. Loseu and J. Rao, 2010 IEEE International Ultrasonics SymposiumProceedings, pp. 1302-1306). However, with as many parameters as areafforded in such a model, it is difficult to find a consistentlypredictive model. In addition, the construction of such a model is timeconsuming and onerous. Furthermore, the model may even be misleading,since the important frequency response of each resonator dependssensitively on the surrounding elements when embedded in a filter. Thus,the primary difficulty with this sophisticated method is the faithfultranslation of the isolated resonator measurements to the sameresonator's response once embedded in a filter or duplexer.

There, thus, remains a need to provide an improved method for modelingacoustic microwave filters over a temperature range.

SUMMARY OF THE INVENTION

In accordance with the present inventions, a method of designing anacoustic microwave filter in accordance with frequency responserequirements is provided. The frequency response requirements maycomprise, e.g., one or more of a frequency dependent return loss,insertion loss, rejection, and linearity. The frequency responserequirements may comprise a pass band, e.g., in the 300 MHz to 300 GHzrange, specifically in the 300 MHz to 10.0 GHz, and more specifically inthe 500-3500 MHz range.

The method comprises generating a proposed filter circuit design havinga plurality of circuit elements comprising an acoustic resonant elementhaving a defined admittance value. The acoustic resonant element may be,e.g., one of a surface acoustic wave (SAW) resonator, a bulk acousticwave (BAW) resonator, a film bulk acoustic resonator (FBAR), and amicroelectromechanical system (MEMS) resonator. The acoustic resonatormay, e.g., be modeled as a Butterworth-Van Dyke (BVD) model, as aCoupling of Modes (COM) model, or a Finite Element Model (FEM). Theproposed filter circuit design may have, e.g., an Nth order laddertopology.

The method further comprises introducing a lumped capacitive element inparallel and a lumped inductive element in series with the resonantelement. The method further comprises selecting a first capacitancevalue for the capacitive element and a first inductance value for theinductive element, thereby creating a first temperature modeled filtercircuit design that shifts the defined admittance value of the resonantelement to a first admittance value, and simulating the firsttemperature modeled filter circuit design at a first operatingtemperature, thereby generating a first frequency response. The methodfurther comprises selecting a second capacitance value for thecapacitive element and a second inductance value for the inductiveelement, thereby creating a second temperature modeled filter circuitdesign that shifts the defined admittance value of the resonant elementto a second admittance value different from the first admittance value,and simulating the second temperature modeled filter circuit design at asecond operating temperature, thereby generating a second frequencyresponse. The first and second capacitance values may be, e.g., in therange of −40 pF-40 pF, and the first and second inductance values maybe, .e.g., in the range of −10 nH-10 nH. An optional method furthercomprises optimizing the proposed filter circuit design, in which case,the lumped capacitive element and lumped inductive element areintroduced into the proposed optimized filter circuit design. The methodfurther comprises comparing the first and second frequency responses tothe frequency response requirements, and constructing the acousticmicrowave filter from the proposed filter circuit design based on thecomparison.

In one embodiment, the first capacitance value and the first inductancevalue are computed as functions of the first operating temperature, andthe second capacitance value and the second inductance value arecomputed as functions of the second operating temperature. For example,the first capacitance value may be selected to be equal to the productof a first scaling factor, the area of the resonant element of theproposed filter circuit design, and the difference between the firstoperating temperature and a baseline temperature; the second capacitancevalue may be selected to be equal to the product of the first scalingfactor, the area of the resonant element of the proposed filter circuitdesign, and the difference between the second operating temperature andthe baseline temperature; the first inductance value may be selected tobe equal to the product of a second scaling factor and the differencebetween the first operating temperature and the baseline temperature;and the second inductance value may be selected to be equal to theproduct of the second scaling factor and the difference between thesecond operating temperature and the baseline temperature.

The scaling factors may be determined in any one of a variety ofmanners. For example, a reference filter circuit design having aplurality of circuit elements comprising a reference acoustic resonantelement can be generated, and a reference acoustic microwave filter fromthe reference filter circuit design can be constructed. The referenceresonant element is composed of the same material as the resonantelement of the proposed filter circuit design. A reference frequencyresponse of the reference acoustic microwave filter can be measured at areference operating temperature, and each of the first and secondscaling factors can be computed based on the reference frequencyresponse.

For example, a lumped reference capacitive element can be introduced inparallel and a lumped reference inductive element in series with thereference resonant element, and selecting a reference capacitance valuefor the lumped reference capacitive element and a reference inductancevalue for the lumped reference inductive element, thereby generating atemperature modeled reference filter circuit design. The temperaturemodeled reference filter circuit design can then simulated at thereference operating temperature while changing the reference capacitancevalue and the reference inductance value until a frequency response ofthe simulated reference filter circuit design matches the measuredfrequency response of the temperature modeled reference acousticmicrowave filter at the reference operating temperature, therebyarriving at a final reference capacitance value and a final referenceinductance value. The first scaling factor may equal the final referencecapacitance value divided by the product of the area of the referenceresonant element and the difference between the reference operatingtemperature and the baseline operating temperature, and the secondscaling factor may equal the final reference inductance value divided bythe difference between the reference operating temperature and thebaseline operating temperature.

Other and further aspects and features of the invention will be evidentfrom reading the following detailed description of the preferredembodiments, which are intended to illustrate, not limit, the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate the design and utility of preferred embodimentsof the present invention, in which similar elements are referred to bycommon reference numerals. In order to better appreciate how theabove-recited and other advantages and objects of the present inventionsare obtained, a more particular description of the present inventionsbriefly described above will be rendered by reference to specificembodiments thereof, which are illustrated in the accompanying drawings.

Understanding that these drawings depict only typical embodiments of theinvention and are not therefore to be considered limiting of its scope,the invention will be described and explained with additionalspecificity and detail through the use of the accompanying drawings inwhich:

FIG. 1 is a frequency response plot comparing the pass band of anacoustic filter circuit design simulated at different operatingtemperatures;

FIG. 2 is a frequency response plot comparing the pass band of anacoustic filter circuit design simulated at different operatingtemperatures to the pass band of an actual acoustic filter measured atthe same operating temperatures;

FIG. 3 is a block diagram of a wireless telecommunications system;

FIG. 4 is a flow diagram of a technique used to design a microwaveacoustic filter for use in the wireless telecommunications system ofFIG. 3;

FIG. 5 is a schematic diagram of a conventional microwave acousticfilter arranged in an Nth order ladder topology;

FIG. 6 is a schematic diagram illustrating the transformation of anacoustic resonator of the acoustic filter of FIG. 5 into an equivalentmodified Butterworth-Van Dyke (MBVD) model;

FIG. 7 is a schematic diagram illustrating the MBVD equivalent circuitof the conventional acoustic filter of FIG. 5;

FIG. 8 is a schematic diagram illustrating an acoustic resonator havingtemperature compensating lumped circuit elements;

FIG. 9 is a schematic diagram illustrating the transformation of thetemperature modeled acoustic resonator of FIG. 8 into an equivalentmodified Butterworth-Van Dyke (MBVD) model;

FIG. 10 is a schematic diagram illustrating a temperature modeledacoustic filter circuit design using the acoustic resonator of FIG. 8;

FIG. 11 is a flow diagram illustrating a technique for computing scalingfactors for the temperature modeled lumped circuit elements;

FIG. 12 is a frequency response plot comparing the pass band of anacoustic filter circuit design designed in accordance with the techniqueillustrated in FIG. 4 to the pass band of an actual acoustic filterconstructed from the acoustic filter circuit design; and

FIG. 13 is a block diagram of a computerized filter design system thatcan implement the computerized steps of the filter design technique ofFIG. 4.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present disclosure describes a technique for designing acoustic wave(AW) microwave filters (such as surface acoustic wave (SAW), bulkacoustic wave (BAW), film bulk acoustic resonator (FBAR),microelectromechanical system (MEMS) filters)). This technique can beapplied to AW microwave filters in the 300 MHz to 300 GHz frequencyrange, particularly in the 300 MHz to 10.0 GHz frequency range, and evenmore particularly in the 500 MHz to 3.5 GHz frequency range. Such AWmicrowave filters may be either fixed frequency and/or tunable filters(tunable in frequency and/or bandwidth and/or input impedance and/oroutput impedance), and may be used for single band or multiple bandbandpass filtering and/or bandstop. Such AW microwave filters areadvantageous in applications that have demanding electrical and/orenvironmental performance requirements and/or severe cost/sizeconstraints, such as those found in the radio frequency (RF) frontendsof mobile communications devices, including cellphones, smartphones,laptop computers, tablet computers, etc. or the RF front ends of fixedcommunications devices, including M2M devices, wireless base stations,satellite communications systems, etc.

Example AW microwave filters described herein exhibit a frequencyresponse with a single passband, which is particularly useful intelecommunication system duplexers. For example, with reference to FIG.3, a telecommunications system 10 for use in a mobile communicationsdevice may include a transceiver 12 capable of transmitting andreceiving wireless signals, and a controller/processor 14 capable ofcontrolling the functions of the transceiver 12. The transceiver 12generally comprises a broadband antenna 16, a duplexer 18 having atransmit filter 24 and a receive filter 26, a transmitter 20 coupled tothe antenna 16 via the transmit filter 24 of the duplexer 18, and areceiver 22 coupled to the antenna 16 via the receive filter 26 of theduplexer 18.

The transmitter 20 includes an upconverter 28 configured for convertinga baseband signal provided by the controller/processor 14 to a radiofrequency (RF) signal, a variable gain amplifier (VGA) 30 configured foramplifying the RF signal, a bandpass filter 32 configured for outputtingthe RF signal at an operating frequency selected by thecontroller/processor 14, and a power amplifier 34 configured foramplifying the filtered RF signal, which is then provided to the antenna16 via the transmit filter 24 of the duplexer 18.

The receiver 22 includes a notch or stopband filter 36 configured forrejecting transmit signal interference from the RF signal input from theantenna 16 via the receiver filter 26, a low noise amplifier (LNA) 38configured for amplifying the RF signal from the stop band filter 36with a relatively low noise, a bandpass filter 40 configured foroutputting the amplified RF signal at a frequency selected by thecontroller/processor 14, and a downconverter 42 configured fordownconverting the RF signal to a baseband signal that is provided tothe controller/processor 14. Alternatively, the function of rejectingtransmit signal interference performed by the stop-band filter 36 caninstead be performed by the duplexer 18. Or, the power amplifier 34 ofthe transmitter 20 can be designed to reduce the transmit signalinterference.

It should be appreciated that the block diagram illustrated in FIG. 3 isfunctional in nature, and that several functions can be performed by oneelectronic component or one function can be performed by severalelectronic components. For example, the functions performed by the upconverter 28, VGA 30, bandpass filter 40, downconverter 42, andcontroller/processor 14 are oftentimes performed by a single transceiverchip. The function of the bandpass filter 32 can be performed by thepower amplifier 34 and the transmit filter 24 of the duplexer 18.

The exemplary technique described herein is used to design acousticmicrowave filters for the front-end of the telecommunications system 10,and in particular the transmit filter 24 of the duplexer 18, althoughthe same technique can be used to design acoustic microwave filters forthe receive filter 26 of the duplexer 18 and for other RF filters.

Referring now to FIG. 4, one exemplary technique 50 for designing an AWmicrowave filter will be described. First, the filter requirements,which comprise the frequency response requirements (including passband,return loss, insertion loss, rejection, linearity, noise figure, inputand output impedances, etc.), as well as size and cost requirements, andenvironmental requirements, such as operating temperature range,vibration, failure rate, etc., are established by the application of thefilter (step 52).

Next, the structural types of circuit elements to be used in the AWfilter are selected; for example, the structural type of resonator (SAW,BAW, FBAR, MEMS, etc.) and the types of inductor, capacitor, and switch,along with the materials to be used to fabricate these circuit elements,including the packaging and assembly techniques for fabricating thefilter, are selected (step 54). In the particular example describedherein, the selection of circuit element types are SAW resonators andcapacitors constructed on a substrate composed of 42-degree XY-cutLiTaO3.

Then, an initial filter circuit design is generated based on thefrequency response requirements using a suitable design technique (step56); for instance, using an image design or network synthesis design,such as those described in U.S. Pat. Nos. 8,701,065 and 9,038,005, whichare expressly incorporated herein by reference. In the illustratedembodiment, the proposed filter circuit design has an Nth order laddertopology, such as those described in U.S. Pat. Nos. 8,751,993 and8,701,065 and U.S. patent application Ser. No. 14/941,451, entitled“Acoustic Wave Filter with Enhanced Rejection”, which are all expresslyincorporated herein by reference; although other filter topologies, suchas in-line non-resonant-node, or in-line, or in-line with crosscouplings, or in-line non-resonant node with cross couplings, etc., maybe selected.

Referring now to FIG. 5, one embodiment of a filter circuit design 100will be described. The filter circuit design 100 is arranged in anNth-order ladder topology (i.e., in this case, N=10 meaning the numberof resonators equals 10). The filter circuit design 100 comprises avoltage source V, a source resistance S, a load resistance L, fiveseries (or in-line) acoustic resonators Z_(S1)-Z_(S5), and five parallel(or in-shunt) acoustic resonators Z_(P1)-Z_(P5).

Each of the acoustic resonators Z may be described by a modifiedButterworth-Van Dyke (MBVD) model 110 illustrated in FIG. 6, therebyresulting in the equivalent filter circuit design illustrated in FIG. 7.MBVD models 110 may also describe SAW resonators, which may befabricated by disposing interdigital transducers (IDTs) on apiezoelectric substrate, such as crystalline Quartz, Lithium Niobate(LiNbO₃), Lithium Tantalate (LiTaO₃) crystals or BAW (including FBAR)resonators or MEMS resonators. Each MBVD model 110 includes a motionalcapacitance C_(m), a static capacitance C₀, a motional inductance L_(m),and a resistance R. The motional capacitance C_(m) and motionalinductance L_(m) may result from the interactions of electrical andacoustical behavior, and thus, may be referred to as the motional arm ofthe MBVD model. The static capacitance C₀ may result from thecapacitance of the structure, and thus, may be referred to as the static(non-motional) capacitance of the MBVD model. The resistance R mayresult from the electrical resistance of the acoustic resonator.Alternatively, rather than using an MBVD model, the acoustic resonatormay be an arbitrary one-port impedance produced by other types ofsuitable models, such as a Coupling-of-Modes (COM) model or FiniteElement Model (FEM).

The parameters of the MBVD model 110 are related by the followingequations:

$\begin{matrix}{{\omega_{R} = \frac{1}{\sqrt{L_{m}C_{m}}}};} & \lbrack 1\rbrack \\{\frac{\omega_{A}}{\omega_{R}} = \sqrt{{1 + \frac{1}{\gamma}},}} & \lbrack 2\rbrack\end{matrix}$

where ω_(R) and ω_(A) may be the respective resonance and anti-resonancefrequencies for any given acoustic resonator, and gamma γ may depend ona material's property, which may be further defined by:

$\begin{matrix}{\frac{C_{0}}{C_{m}} = {\gamma.}} & \lbrack 3\rbrack\end{matrix}$

Typical γ values may range from about 12 to about 18 for 42-degree X Ycut LiTaO₃. The frequency separation of an acoustic resonator means thedifference between its resonant frequency and its anti-resonantfrequency. The percentage separation of an acoustic wave resonator isthe percentage frequency separation between its resonant frequency andanti-resonant frequency, and can be computed, as follows:

percentage separation=√{square root over (1+(1/γ))}−1  (4)

where γ is the ratio of the static to the motional capacitance of theresonator (equation [3]), as determined by the material properties ofthe piezoelectric material and modified by the geometry of the device.

It can be appreciated from equation [1] that the resonant frequency ofeach of the acoustic resonators will depend on the motional arm of theBVD model 110, whereas the filter characteristics (e.g., bandwidth) willbe strongly influenced by γ in equation [2]. The Quality factor (Q) foran acoustic resonator 110 may be an important figure of merit inacoustic filter design, relating to the loss of the element within thefilter. Q of a circuit element represents the ratio of the energy storedper cycle to the energy dissipated per cycle. The Q factor models thereal loss in each acoustic resonator, and generally more than one Qfactor may be required to describe the loss in an acoustic resonator. Qfactors may be defined as follows for the filter examples. The motionalcapacitance C_(m) may have an associated Q defined as Q_(cm)=10⁸; thestatic capacitance C₀ may have an associated Q defined as Q_(c0)=200;and motional inductance L_(m) may have an associated Q defined asQ_(Lm)=1000. (Here for simplicity the loss in the motional resonance islumped into the motional inductance and the motional capacitance isconsidered to be essentially loss-less.) Circuit designers may typicallycharacterize SAW resonators by resonant frequency ω_(R), staticcapacitance C₀, gamma γ, and Quality factor QL_(m). For commercialapplications, QL_(m) may be about 1000 for SAW resonators, and about3000 for BAW resonators.

Referring back to FIG. 4, the filter circuit design 100 is nextoptimized via a suitable computer optimization technique to search forthe combination of circuit element values that best matches the desiredfilter response, thereby creating a proposed filter circuit designhaving defined values for all of the circuit elements, includingadmittance values for the acoustic resonators Z (step 58). Design tools,including Agilent Advanced Design System (ADS), among others, may usenumerical optimization methods, such as Monte Carlo, gradient, etc., toimprove the proposed filter circuit design. In one embodiment, one ormore circuit elements in the proposed filter circuit design can beremoved during the optimization process, such as disclosed in U.S. Pat.No. 8,751,993, which has been expressly incorporated herein byreference.

The effects of temperature variations on the proposed filter circuitdesign can be simulated by adding two discrete components to eachacoustic resonator Z in the filter: a series inductor to shift theresonant frequency of the respective acoustic resonator Z, and aparallel capacitor to shift the anti-resonant frequency of therespective acoustic resonator Z. In particular, a lumped capacitiveelement C_(T) is introduced in parallel and a lumped inductive elementL_(T) is introduced in series with each acoustic resonator Z of theproposed filter circuit design (FIG. 8) to create a temperature modeledfilter circuit design 200, as illustrated in FIG. 10 (step 60). Asillustrated in FIG. 9, each of the acoustic resonators Z of thetemperature modeled filter design 200 can be replaced with the MBVDmodel 110 illustrated in FIG. 6.

Next, a selected number of temperature modeled circuit designscorresponding to different operating temperatures (e.g., three operatingtemperatures of 0° C., 20° C., and 100° C.) are created and simulated byvarying the capacitance values for the capacitive elements C_(T) andinductance values for the inductive elements L_(T) for each respectiveoperating temperature to be simulated. The capacitance values andinductances values for each operating temperature can be computed as afunction of that operating temperature. In one embodiment, thecapacitance value for each capacitive element C_(T) and the inductancevalue for each inductive element L_(T) are computed in accordance withthe following equations:

C _(Tn) =k _(C) ·A _(n)·(T _(op) −T _(base)),  [6]

where C_(Tn) is the capacitance value of the nth acoustic resonator inthe temperature modeled filter circuit design, k_(C) is a scalingconstant for the capacitive elements, A_(n) is the area of the nthacoustic resonator, T_(op) is the operating temperature, and T_(base) isa baseline temperature at which it is assumed that C_(Tn) equals zero(e.g., room temperature); and

L _(Tn) =k _(L)·(T _(op) −T _(base)),  [7]

where L_(Tn) is the inductance value of the nth acoustic resonator inthe temperature modeled filter circuit design, k_(L) is a scalingconstant for the inductive elements, T_(op) is the operatingtemperature, and T_(base) is a baseline temperature at which it isassumed that L_(Tn) equals zero (e.g., room temperature).

To this end, capacitance values for the capacitive elements C_(T) andinductance values for the respective inductive elements L_(T) areselected, thereby creating a temperature modeled filter circuit designthat shifts the defined admittance values of the respective acousticresonators Z to different admittance values (step 62). As a generalrule, the inductance values for all of the inductive elements L_(T) willbe the same, whereas the capacitance values for all of the capacitiveelements C_(T) will be the same only if the areas of the acousticresonators Z are the same. The temperature modeled filter circuit designis then simulated at a defined operating temperature, thereby generatinga frequency response (step 64). The first and second capacitance valuesmay be, e.g., in the range of −40 pF-40 pF, and more specifically in therange of −4 pF-4 pF, and the first and second inductance values may be,.e.g., in the range of −10 nH-10 nH, and more specifically in the rangeof −1 nH-1 nH.

Additional temperature modeled filter circuit designs corresponding todifferent operating temperatures can be created by selecting differentcapacitance values and inductance values. In particular, if not all theselected number of operating temperatures have been simulated (i.e., ifnot all of the temperature modeled filter circuit designs have beensimulated) (step 66), different capacitance values for the capacitiveelements C_(T) and inductance values for the respective inductiveelements L_(T) are selected, thereby creating another temperaturemodeled filter circuit design that shifts the defined admittance valuesof the respective acoustic resonators Z to different admittance values(step 62), and then the other temperature modeled filter circuit designis simulated at another defined operating temperature, therebygenerating a frequency response (step 64). This process is repeateduntil all of the temperature modeled filter circuit designs have beensimulated. If the simulated frequency responses of the temperaturemodeled filter circuit designs do not satisfy the frequency responserequirements at the defined operating temperatures (step 68), adifferent initial filter circuit design may be generated and optimizedto create another proposed filter circuit design (steps 56 and 58) andthen, temperature modeled filter circuit designs can be generated fromthe other proposed filter circuit design and simulated (steps 60-66).Once the simulated frequency responses of the temperature modeled filtercircuit designs satisfy the frequency response requirements at thedefined operating temperatures (step 68), an actual acoustic filter isconstructed based on the most recent proposed filter circuit design(step 70). Preferably, the circuit element values of the actual acousticfilter will match the corresponding circuit element values in the mostrecent proposed filter circuit design.

The scaling factors k_(C) and k_(L) of equations [6] and [7] can bedetermined by measuring the frequency responses of an actual acousticfilter and fitting data of simulated temperature-compensated filtercircuits to the frequency responses of the actual acoustic filter. Inparticular, with reference to FIG. 11, one technique 80 for determiningthe scaling factors k_(C) and k_(L) will now be described. First, areference filter circuit design having a plurality circuit elementscomprising at least one acoustic resonator is generated (step 82), andthen, an actual reference acoustic microwave filter is constructed fromthe reference filter circuit design (step 84). The acoustic resonator(s)of this reference filter are composed of the same material as theacoustic resonators of the proposed filter circuit design 100, so thatthe scaling factors determined from the reference filter can beaccurately used to generate the temperature modeled filter designs 200from the proposed filter circuit design 100. Next, a reference frequencyresponse of the actual reference filter is measured at a reference(e.g., room temperature) (step 86).

Each of the first and second scaling factors k_(C) and k_(L) is thencomputed based on the first reference frequency response. In particular,a lumped reference capacitive element is added in parallel and a lumpedreference inductive element is added in series with each of thereference acoustic resonator(s) in a similar manner as the capacitiveelement(s) and inductive elements(s) are added to the proposed filtercircuit design 100 in FIG. 5, thereby generating a reference temperaturemodeled filter circuit design (step 88).

Then, the capacitance value of the reference capacitive element(s) andthe reference inductance value of the reference inductive elements(s)that match the simulated frequency response of the temperature modeledreference filter circuit design at the reference operating temperatureto the measured frequency response of the actual reference acousticfilter is determined (step 90). For example, the temperature modeledreference filter circuit design can be iteratively simulated at thereference operating temperature while changing the capacitance value ofthe reference capacitive element(s) and the reference inductance valueof the reference inductive element(s) until the frequency response ofthe simulated temperature modeled reference filter circuit designmatches the measured frequency response of the reference acousticmicrowave filter at the reference operating temperature, therebyarriving at a first reference capacitance value C_(REF1) and a firstreference inductance value L_(REF1).

The first scaling factor k_(C) is then computed in accordance with thefollowing equation (step 92):

$\begin{matrix}{{k_{C} = \frac{C_{REF}}{A \cdot ( {T_{REF} - T_{base}} )}},} & \lbrack 8\rbrack\end{matrix}$

where k_(C) is the first scaling factor, C_(REF) is the referencecapacitance value, A is the area of the reference acoustic resonator,T_(REF) is the reference operating temperature, and T_(base) is thebaseline operating temperature (e.g., room temperature); and the secondscaling factor k_(L) is then computed in accordance with the followingequation (step 94):

$\begin{matrix}{{k_{L} = \frac{L_{REF}}{( {T_{REF} - T_{base}} )}},} & \lbrack 9\rbrack\end{matrix}$

where k_(L) is the second scaling factor, L_(REF) is the referenceinductance value, T_(REF) is the reference operating temperature, andT_(base) is the baseline operating temperature.

It should be appreciated that additional scaling factors may be computedfor different operating temperature ranges. For example, a first set ofscaling factors k_(C1) and k_(L1) can be associated with the temperaturerange 0° C.-50° C., and a second set of scaling factors k_(C2) andk_(L2) can be associated with the temperature range 50° C.-100° C. Thefirst set of scaling factors k_(C1) and k_(L1) can be determined bymeasuring the frequency response of the reference filter in accordancewith equations [8] and [9] using, e.g., 25° C. as the referenceoperating temperature; and the second set of scaling factors k_(C2) andk_(L2) can be determined by measuring frequency responses of thereference filter at two reference operating temperatures (e.g., 50° C.and 100° C.), iteratively simulating the temperature modeled referencefilter circuit design at the first reference temperature while changingthe capacitance value of the reference capacitive element(s) and thereference inductance value of the reference inductive element(s) untilthe frequency response of the simulated temperature modeled referencefilter circuit design matches the measured frequency response of thereference acoustic microwave filter at the first reference operatingtemperature, thereby arriving at a first reference capacitance valueC_(REF1) and a first reference inductance value L_(REF1), anditeratively simulating the temperature modeled reference filter circuitdesign at the second reference temperature while changing thecapacitance value of the reference capacitive element(s) and thereference inductance value of the reference inductive element(s) untilthe frequency response of the simulated temperature modeled referencefilter circuit design matches the measured frequency response of thereference acoustic microwave filter at the second reference temperature,thereby arriving at a second reference capacitance value C_(REF2) and asecond reference inductance value L_(REF1).

The scaling factor k_(C2) is then computed in accordance with thefollowing equation:

$\begin{matrix}{{k_{C} = \frac{C_{{REF}\; 2} - C_{{REF}\; 1}}{A \cdot ( {T_{{REF}\; 2} - T_{{REF}\; 1}} )}},} & \lbrack 10\rbrack\end{matrix}$

where k_(C) is the scaling factor, C_(REF2) is the second referencecapacitance value, C_(REF1) is the first reference capacitance value, Ais the area of the reference acoustic resonator, T_(REF2) is the secondreference operating temperature (e.g., 100° C.), and T_(REF1) is thefirst reference operating temperature (e.g., 50° C.).

The scaling factor k_(L2) is then computed in accordance with thefollowing equation:

$\begin{matrix}{{k_{L} = \frac{L_{{REF}\; 2} - L_{{REF}\; 1}}{( {T_{{REF}\; 2} - T_{{REF}\; 1}} )}},} & \lbrack 11\rbrack\end{matrix}$

where k_(L) is the scaling factor, L_(REF2) is the second referenceinductance value, L_(REF1) is the first reference inductance value,T_(REF2) is the second reference operating temperature (e.g., 100° C.),and T_(REF1) is the first reference operating temperature (e.g., 50°C.).

The acoustic microwave filter design illustrated in FIG. 5 was optimizedin accordance with the technique illustrated in FIG. 4, and then anactual acoustic microwave filter was constructed from the optimizedacoustic microwave filter design. Referring to FIG. 12, the frequencyresponses of the acoustic microwave filter design simulated at −20° C.and 100° C. (dashed lines) can be compared to the frequency responses ofthe corresponding actual acoustic microwave filter measured at −20° C.and 100° C. (solid lines). It can be readily seen that the left andright sides of the passbands of the simulated frequency responses at−20° C. and 100° C. respectively match the left and right sides of thepassbands of the actual frequency responses at −20° C. and 100° C.

Referring first to FIG. 13, a computerized filter design system 300 maybe used to design an acoustic filter using the design technique 50. Thecomputerized filter design system 300 generally comprises a userinterface 302 configured for receiving information and data from a user(e.g., parameter values and filter specifications at steps 52 and 54)and outputting an optimized filter circuit design to the user; a memory304 configured for storing filter design software 308 (which may takethe form of software instructions, which may include, but are notlimited to, routines, programs, objects, components, data structures,procedures, modules, functions, and the like that perform particularfunctions or implement particular abstract data types), as well as theinformation and data input from the user via the user interface 302; anda processor 306 configured for executing the filter design software. Thefilter design software program 308 is divided into sub-programs, inparticular, a conventional filter design synthesizer 310 (which can beused to generate the initial filter circuit design at step 56), aconventional filter optimizer 312 (which can be used to optimize andsimulate the filter design at steps 58 and 64), and a filter designengine 314 that controls the design synthesizer 310 and filter optimizer312 and adds and determines the values of the lumped capacitive andinductive elements at steps 60 and 62 in order to generate the optimizedfinal circuit design.

Although particular embodiments of the present invention have been shownand described, it should be understood that the above discussion is notintended to limit the present invention to these embodiments. It will beobvious to those skilled in the art that various changes andmodifications may be made without departing from the spirit and scope ofthe present invention. For example, the present invention hasapplications well beyond filters with a single input and output, andparticular embodiments of the present invention may be used to formduplexers, multiplexers, channelizers, reactive switches, etc., wherelow-loss selective circuits may be used. Thus, the present invention isintended to cover alternatives, modifications, and equivalents that mayfall within the spirit and scope of the present invention as defined bythe claims.

What is claimed is:
 1. A computerized filter design system for designinga filter circuit design, comprising: a user interface configured forreceiving circuit parameter values and frequency response requirementsfrom a user and outputting a final filter circuit design to the user;memory storing a filter design software program; and a processorconfigured for executing the filter design software program to (a)generate a proposed filter circuit design having a plurality of circuitelements comprising an acoustic resonant element having an admittancevalue derived from the circuit parameter values, (b) introduce a lumpedcapacitive element in parallel and a lumped inductive element in serieswith the acoustic resonant element, (c) selecting a capacitance valuefor the lumped capacitive element and an inductance value for the lumpedinductive element, thereby creating a temperature modeled filter circuitdesign that shifts the defined admittance value of the acoustic resonantelement to an admittance value, (d) simulating the temperature modeledfilter circuit design at an operating temperature, thereby generating afrequency response, (e) comparing the frequency response to thefrequency response requirements, and (f) generating the final filtercircuit design based on the comparison.
 2. The computerized filterdesign system of claim 1, wherein the frequency response requirementscomprise one or more of a frequency dependent return loss, insertionloss, rejection, and linearity.
 3. The computerized filter design systemof claim 1, wherein the acoustic resonant element is one of a surfaceacoustic wave (SAW) resonator, a bulk acoustic wave (BAW) resonator, afilm bulk acoustic resonator (FBAR), and a microelectromechanical system(MEMS) resonator.
 4. The computerized filter design system of claim 1,wherein the frequency response requirement comprises a pass band.
 5. Thecomputerized filter design system of claim 4, wherein the passband is inthe 500-3500 MHz range.
 6. The computerized filter design system ofclaim 4, wherein the passband is in the 300 MHz to 10.0 GHz range. 7.The computerized filter design system of claim 4, wherein the passbandis in the 300 MHz to 300 GHz range.
 8. The computerized filter designsystem of claim 1, wherein the frequency response requirements comprisea passband and a stopband.
 9. The computerized filter design system ofclaim 1, wherein the processor is configured for executing the filterdesign software program to further model the acoustic resonant elementas a Butterworth-Van Dyke (BVD) model.
 10. The computerized filterdesign system of claim 1, wherein the processor is configured forexecuting the filter design software program to further model theacoustic resonant element with a Coupling of Modes (COM) model.
 11. Thecomputerized filter design system of claim 1, wherein the processor isconfigured for executing the filter design software program to furthermodel the acoustic resonant element with a Finite Element Model (FEM).12. The computerized filter design system of claim 1, wherein theproposed filter circuit design has an Nth order ladder topology.
 13. Thecomputerized filter design system of claim 1, wherein the capacitancevalue and the inductance value are selected as functions of theoperating temperature.
 14. The computerized filter design system ofclaim 13, wherein the capacitance value is selected to be equal to theproduct of a first scaling factor, the area of the acoustic resonantelement of the proposed filter circuit design, and the differencebetween the operating temperature and a baseline temperature, and theinductance value is selected to be equal to the product of a secondscaling factor and the difference between the operating temperature andthe baseline temperature.
 15. The computerized filter design system ofclaim 1, wherein the capacitance value is in the range of range of −40pF-40 pF.
 16. The computerized filter design system of claim 1, whereinthe capacitance value is in the range of range of −4 pF-4 pF.
 17. Thecomputerized filter design system of claim 1, wherein the inductancevalue is in the range of −10 nH-10 nH.
 18. The computerized filterdesign system of claim 1, wherein the inductance value is in the rangeof −1 nH-1 nH.
 19. The computerized filter design system of claim 1,wherein the processor is configured for executing the filter designsoftware program to generate an initial filter circuit design having thecircuit parameter values, and optimizing the initial filter circuitdesign to create the proposed filter circuit design, wherein the lumpedcapacitive element and lumped inductive element are introduced into theproposed optimized filter circuit design.
 20. The computerized filterdesign system of claim 19, wherein the filter design software program isdivided into a filter design synthesizer, a filter optimizer, and afilter design engine, wherein the processor is configured for executingthe filter design synthesizer to generate the initial filter circuitdesign, for executing the filter optimizer to optimize the initialfilter circuit to create the proposed filter circuit design, andsimulating the temperature modeled filter circuit design at theoperating temperature, thereby generating the frequency response, andfor executing the filter design engine to introduce the lumpedcapacitive element in parallel and the lumped inductive element inseries with the acoustic resonant element, selecting the capacitancevalue for the lumped capacitive element and the inductance value for thelumped inductive element, thereby creating the temperature modeledfilter circuit design, comparing the frequency response to the frequencyresponse requirements, and generating the final filter circuit designbased on the comparison.